Some Results on Conditionally Compatible and Conditionally Semi-Compatible Mappings in Probabilistic 2-Metric Space
DOI:
https://doi.org/10.26713/cma.v13i1.1709Keywords:
(E.A)-property, Conditionally compatible, Conditionally semi-compatible, Sub-sequentially continuous, Probabilistic 2-metric spaceAbstract
The objective of this paper is to obtain two results in probabilistic 2-metric space by employing the concepts of (E.A)-property, conditionally compatible, conditionally semi-compatible and sub-sequentially continuous mappings. These findings improve the theorem proved in [5]. Further, these results are substantiated by supporting examples.
Downloads
References
C. Alsina, B. Schweizer and A. Sklar, On the definition of a probabilistic normed space, Aequationes Mathematicae 46 (1993), 91 – 98, DOI: 10.1007/BF01834000.
R.K. Bisht and N. Shahzad, Faintly compatible mappings and common fixed points, Fixed Point Theory and Applications 2013 (2013), Article number: 156, DOI: 10.1186/1687-1812-2013-156.
S. Gähler, 2-metrische Räume und ihre topologische Struktur, Mathematische Nachrichten 26(1-4) (1963), 115 – 148, DOI: 10.1002/mana.19630260109.
I. Golet, Fixed point theorems for multivalued mapping in probabilistic 2-metric spaces, Analele Stiintifice ale Universitatii Ovidius Constanta 3 (1995), 44 – 51.
V.K. Gupta, A. Jain and R. Kumar, Common fixed point theorem in probabilistic 2-Metric space by weak compatibility, International Journal of Theoretical and Applied Sciences 11 (2019), 9 – 12.
M.K. Jain and M.S. Khan, Generalization of semi compatibility with some fixed point theorems under strict contractive condition, Applied Mathematics E-Notes 17 (2017), 25 – 35.
K. Menger, Statistical metrics, Proceedings of the National Academy of Sciences of the United States of America 28(12) (1942), 535 – 537, DOI: 10.1073/pnas.28.12.535.
S.N. Mishra, Common fixed points of compatible mappings in PM-spaces, Mathematica Japonica 36 (1991), 283 – 289.
K. Satyanna and V. Srinivas, Fixed point theorem using semi compatible and sub-sequentially continuous mappings in Menger space, Journal of Mathematical and Computational Science 10(6) (2020), 2503 – 2515, DOI: 10.28919/jmcs/4953.
V.M. Sehgal and A.T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric spaces, Mathematical Systems Theory 6 (1972), 97 – 102, DOI: 10.1007/BF01706080.
B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, Journal of Mathematical Analysis and Applications 301(2) (2005), 439 – 448, DOI: 10.1016/j.jmaa.2004.07.036.
V. Srinivas, T. Tirupathi and K. Mallaiah, A fixed point theorem using EA property on multiplicative metric space, Journal of Mathematical and Computational Science 10 (2020), 1788 – 1800, DOI: 10.28919/jmcs/4752.
Z. Xiaohong, H. Huacan and X. Yang, A fuzzy logic system based on Schweizer-Sklar t-norm, Science in China Series F: Information Sciences 49 (2006), 175 – 188, DOI: 10.1007/s11432-006-0175-y.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
